The present invention is generally directed to printing technology and more particularly to the prediction of color values producible by a printer under a target set of operating conditions.
FIG. 1 is a stylized pictorial representation of a prior art printing system generally indicated by the reference character 10 for producing a printed image 12 on a substrate 14. The printing system 10 includes a printer device 16 operable under control of a controller 18. The printer device 16 can be any device capable of placing a colored material on a substrate. For example, the printing device may be implemented an ink jet printer, a dye sublimation printer, a color laser printer or an offset press, among others.
A predetermined set 20 of colorants is available to the printer 16 for deposition on the substrate 14. For example, in a typical instance the set 20 of colorants includes a cyan-colored (sky blue) ink (“C”), a magenta-colored (red) ink (“M”), a yellow-colored ink (“Y”) and a black-colored ink (“K”). Colorants in addition to or in substitution for these aforementioned typical four colorants may also be used.
The controller 18 is the computational engine that serves to convert color information on a source image 26 rendered on a substrate 28 into a format compatible with the printer 16. To this end the controller 18 includes at least one color characterization table 30, typically referred to as a “B-to-A” table.
In addition, depending upon the color model used for the source image 26, an additional forward transform table 34, known as a “A-to-B” table, may be required. The forward transform is used to map from the color model of the source image to a device-independent color model such as CIE L*a*b* color values or X, Y, Z tri-stimulus values.
The International Committee on Illumination (CIE) L*a*b* system is a three-dimensional system for representing the color of an object in terms of color parameters arranged along three mutually orthogonal coordinate axes, viz., L*, a*, and b*. The L* axis is the lightness axis and ranges from values of 0 to 100 (black to white). The a* axis extends from red (+a) to green (−a), while the b* axis extends from yellow (+b*) to blue (−b*). A complete description of the CIE L*a*b* system is found in CIE Publication 15.2 or in various standards collections such as ASTM E-308.
The X, Y, Z tri-stimulus values define a mapping standardized by the International Committee on Illumination (CIE) that is based upon the manner in which color is seen by a human observer. The human eye has three sensors for color vision—a blue sensor, a green sensor and a red sensor. Color perception is dependent not only on the spectral curve of the reflectance from the colored object but also the spectral characteristics of the light source under which it is viewed and the spectral sensitivity of the observer. The X, Y, Z tri-stimulus space is a three-dimensional color mapping that incorporates the effect of the spectral characteristics of the colored object, the light source and the observer.
The relationships between the tri-stimulus values X, Y, Z and the CIE L*a*b* values are described by the following equations:L*=116[f(Y/Y0)]−16  (1)a*=500[f(X/X0)−f(Y/Y0)]  (2)b*=200[f(Y/Y0)−f(Z/Z0)]  (3)
where X0, Y0 and Z0 define the reference white point, and where,f(X/X0)=(X/X0)1/3 for X/X0>0.008856f(X/X0)=7.787·(X/X0)+16/116 for X/X0≦0.008856f(Y/Y0)=(Y/Y0)1/3 for Y/Y0>0.008856f(Y/Y0)=7.787·(Y/Y0)+16/116 for Y/Y0≦0.008856f(Z/Z0)=(Z/Z0)1/3 for Z/Z0>0.008856f(Z/Z0)=7.787·(Z/Z0)+16/116 for Z/Z0≦0.008856
In order to produce both an “A-to-B” table 34 and a “B-to-A” table 30 a predetermined number M of samples corresponding to various colorants or combinations of colorants are printed. As used throughout this application the term “sample” means a printed rendition of a color produced by a printer on a substrate using a predetermined colorant or combination of available colorants. Such samples may also be known as “color patches”.
Once produced the spectral reflectance of each sample is measured.
Either the spectral reflectances measured from the samples or, after appropriate conversion using the above equations, their corresponding computed CIE L*a*b* values, together with the respective colorant or combinations of colorants are input to a computing device executing a color characterization program. The color characterization program generates both a forward transform relating input colorants or colorant combinations to output color values, the “A-to-B” table, and the reverse transform, the desired “B-to-A” table, relating desired output color values to device colorant or colorant combinations.
Suitable color characterization programs are commercially available from X-Rite Inc., Grandville Mich., as the Monaco PROFILER, or GretagMacbeth, New Windsor, N.Y., as the GretagMacbeth ProfileMaker. Such color characterization programs produce tables of values in a file format that complies with the specifications developed by the International Color Consortium (“ICC”), Reston, Va. and set forth in ICC.1:2004-10 Image technology colour management, Architecture, profile format, and data structure.
The number M of samples necessary to be produced is governed by the particular application program utilized to create the color characterization. Typically, the number M is on the order of several hundred to several thousand samples, depending upon the number of colorant inks used by the printing system. The requirement for such a large number of samples makes production of a color characterization a costly proposition.
Once created the “B-to-A” table is used to determine the precise colorant or combination of colorants that must be deposited by the printer 16 on predetermined areas of the substrate 14 to reproduce color values on the printed image 12 that are as close to identical as possible to the color values that appear on corresponding areas of the source image 26. The assessment of identity may be objectively measured or, perhaps more importantly, visually assessed by a viewer.
At any given time the operation of the printer 16 occurs under the influence of a host of various operating conditions. As used herein the term “operating condition” identifies a printing environment in which all the parameters and factors that influence the printer performance have been held at specified constant values.
The substrate 14/28 (FIG. 1) upon which the image 12/26 is rendered is one such parameter that influences printer performance. For example, the substrates may be paper, fabric, or vinyl. In the fabric arena alone possible fabric substrates could include fabrics made from natural materials (e.g., cotton, silk) or synthetic materials (e.g., nylon, Lycra® fiber), all in various weaves, weights and densities. The fabric substrate may be treated with any of a variety of pre- and/or post-treatments to achieve desirable properties such as pigment binding or water-fastness.
Environmental factors such as temperature and humidity are parameters that affect the printer, primarily modifying ink jetting, ink drop volume, and precision of ink deposition. Printing parameters, such as printing resolution (both along and across the substrate), uni- or bi-directional ink deposition, single or multiple carriages, and the number of nozzles passing over a given area on the substrate also affect the detailed placement of the ink drops.
As another dimension of the problem the printer 16 must be able to achieve color identity at corresponding locations between printed and source images over a wide range of the operating conditions. That is to say, the color value at the same relative location on each of two different images 12, 12′ produced by the printer 16 when operating under respective differing sets of operating conditions must be as close to identical as possible to the color value at the corresponding location on the source image 26. In addition, and perhaps more importantly, the color value at the same relative location on one image 12 must be as close to identical as possible to the color value at the corresponding location on the other image 12′, regardless of the operating conditions.
To achieve this color identity between or among output images produced under different operating conditions the controller 18 includes additional “B-to-A” table(s) 30′, each for a different set of operating conditions. Thus, each “B-to-A” table 30, 30′, as the case may be, determines for a respective set of operating conditions the precise colorant or combinations of colorants that must be deposited by the printer 16 to reproduce on respective printed images 12, 12′ color values that are as close to identical as possible to the color values of the source image 26 and to each other.
One way to produce an alternative “B-to-A” table 30′ is to create an entire set of M samples that characterizes the printer operation under the target set of operating conditions. The measured reflectances (or color values) from these samples are applied to the color characterization program to produce the forward and reverse transforms. Thus, an entire set of M samples is required to obtain a color characterization table for each of the multiple expected sets of target operating conditions. It is clear that production of a plurality of color characterization tables in this way is extremely costly.
An alternative way to create a color characterization for a different target set of operating conditions without printing a sample for all of the different colorants or combinations of colorants is disclosed in U.S. Pat. No. 6,654,143 (Dalal et al.) and in Shaw et al., “Color Printer Characterization Adjustment for Different Substrates”, Color Research and application Volume 28, Number 6, December 2003. In this patent and article a relatively small number of samples is produced under both a first, reference, set of printer operating conditions and a second, target, set of printer operating conditions.
A principal component analysis is applied to a reflectance data set derived from a relatively large number of samples produced under the reference operating conditions. The principal component analysis performed on the large data set is used to compute a number P of principal components (“basis vectors”) to be utilized in further computations.
A second, relatively small, data set is produced or selected from samples produced under the reference operating conditions. A third data set is derived from samples produced under the target operating conditions. The reflectance of each sample in the second and third set of samples is measured as a function of wavelength. The second and third data sets must include the same number of samples and must be produced using the same colorants or colorant combinations.
Thereafter, the first P number of principal components from the first (large) data set are used to project the reflectances from the second and third data sets into the P-dimensional principal component “scores” space. Multiple linear regression is used to compute a least-squares model mapping of the second data set's scores to those of the third data set. The resulting “T” matrix contains P*P coefficients to map from reference to target conditions in the P-dimensional scores space. Computed scores for the target conditions can then be transformed back to the full-dimensional reflectance space by using the inverse of the principal component projection operator.
The application of a principal component analysis tool in this way is believed to be disadvantageous because the choice of the number P of basis vectors is heuristically selected based upon the large sample set, while the mapping from reference to target conditions is derived from the smaller sample sets. It is also believed disadvantageous to perform the analysis in the non-physical “scores” space rather than in a space that correlates with human visual perception, such as a space that uses actual or scaled reflectance.
In view of the foregoing it is believed advantageous to generate a color characterization model for a printer operable under a predetermined target set of operating conditions that maps parameters when the objective function is more closely tied to human vision, as in reflectance space, and which does not arbitrarily select the number of principal factors, but instead relies upon cross-validation to obtain a model of appropriate complexity. It is believed to be of still further advantage to map parameters that are suitably scaled to better match perceived color.
In another aspect, it is believed more efficient and therefore advantageous to be able to produce a mapping from a only predetermined minimum number of samples produced under a given set of target conditions.